Approximating Automata and Discrete Control for Continuous Systems — Two Examples from Process Control

  • Jörg Raisch
  • Eberhard Klein
  • Christian Meder
  • Alexander Itigin
  • Siu O’Young
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1567)


A standard problem in hybrid control systems theory is to design discrete, or symbolic, feedback for a given continuous plant.When specifications are discrete, this problem can be solved by first approximating the continuous plant model by a (nondeterministic) automaton, and then synthesizing discrete (supervisory) control for the automaton. A necessary condition is that the approximation behaviour contains the behaviour of the underlying continuous plant model. Then, any controller forcing the approximation to obey the specifications will also force the continuous model to satisfy the specifications. We use a version of this approach which allows adjustment of approximation accuracy to address two simple process control problems: supervisory control of a three-tank laboratory experiment and safety enforcement for an evaporator. In both cases, the entire design process is carried through: we first determine a suitable abstraction, compute the minimally restrictive supervisor, and then present examples for closed loop trajectories.


Sodium Chloride Solution Discrete Approximation Supervisory Control Discrete Event System Sampling Instant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    P. J. Antsaklis, J. A. Stiver, and M. Lemmon. Hybrid system modelling and autonomous control systems. In [6], pages 366–392.Google Scholar
  2. 2.
    P. Antsaklis, W. Kohn, A. Nerode, and S. Sastry, editors. Hybrid Systems Iv, Lecture Notes in Computer Science, Vol. 1273. Springer-Verlag, 1997.Google Scholar
  3. 3.
    B. A. Brandin and W. M. Wonham. Supervisory control of timed Discrete Event Systems. IEEE Trans. Automat. Contr., vol. 39, pp. 329–342, 1994.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    J. C. Chou. Thermodynamic Properties of Aqueous Sodium Chloride Solutions from 32 to 350 F. Ph. D Thesis, Oklahoma State University, 1968.Google Scholar
  5. 5.
    K. Feldkamp Der Wärmeübergang beim Sieden von wässrigen Lösungen. Ph. D Thesis, Technische Universität Carolo-Wilhelmina, Braunschweig, 1969.Google Scholar
  6. 6.
    R. L. Grossman, A. Nerode, A. P. Ravn, and H. Rischel, editors, Hybrid Systems, Lecture Notes in Computer Science, Vol. 736. Springer-Verlag, 1993.Google Scholar
  7. 7.
    H.-M. Hanisch and S. Kowalewski. Diskontinuierlicher Misch-und Trennprozeß, Fallbeispiel für die Modellierung ereignisdiskreter Systeme und den systematischen Entwurf von Steuerungen. In: 3. Workshop GMA-Fachausschuß 1.8: Methoden der Steuerungstechnik. 1994.Google Scholar
  8. 8.
    T. Kailath, Linear Systems. Prentice-Hall, 1980.Google Scholar
  9. 9.
    J. Lunze. Qualitative modelling of linear dynamical systems with quantized state measurements. Automatica, 30:417–431, 1994.zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    I. N. Maksimova Determination of the Density of Aqueous Solutions. Russian Journal of Physical Chemistry, 39(3): 296–297, 1965.Google Scholar
  11. 11.
    J. Raisch. Nondeterministic automata as approximations for continuous systems-an approach with an adjustable degree of accuracy. Proc. 2nd MATHMOD (International Symposium on Mathematical Modelling), pp. 195–202. IMACS, Vienna. 1997.Google Scholar
  12. 12.
    J. Raisch and S. O’Young. A Totally Ordered Set of Discrete Abstractions for a given Hybrid or Continuous System. In [2], pp. 342–360.Google Scholar
  13. 13.
    J. Raisch and S. D. O’Young. Discrete approximation and supervisory control of continuous systems. Accepted for publication in IEEE Transactions on Automatic Control, Special Issue on Hybrid Systems.Google Scholar
  14. 14.
    J. Raisch. A Hierarchy of Discrete Abstractions for a given Hybrid Plant Model. Proc. ADPM’98 (Automatisation des Processus Mixtes: les Systèmes Dynamiques Hybrides), Reims, March 1998.Google Scholar
  15. 15.
    P. J. Ramadge and W. M. Wonham. Supervisory control of a class of discrete event systems. SIAM J. Control and Optimization, 25:206–230 1987.zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    P. J. Ramadge and W. M. Wonham. The control of discrete event systems. Proceedings of the IEEE, 77:81–98, 1989.CrossRefGoogle Scholar
  17. 17.
    J. A. Stiver and P. Antsaklis. Modeling and analysis of hybrid control systems. In Proc. 31st IEEE Conference on Decision and Control, 1992.Google Scholar
  18. 18.
    Verein Deutscher Ingenieure (VDI)-Gesellschaft Verfahrenstechnik und Chemieingenieurswesen (GVC) (ed.) VDI-Wärmeatlas. VDI-Verlag, Frankfurt, edition, 1988.Google Scholar
  19. 19.
    J. C. Willems. Paradigms and puzzles in the theory of dynamical systems. IEEE Transactions on Automatic Control, 36:259–294, 1991.zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    I. D. Zaytsev and G. G. Aseyev Properties of Aqueous Solutions of Electrolytes. CRC Press, Boca Raton, 1992.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Jörg Raisch
    • 1
  • Eberhard Klein
    • 2
  • Christian Meder
    • 2
  • Alexander Itigin
    • 2
  • Siu O’Young
    • 3
  1. 1.Max-Planck-Institut für Dynamik komplexer technischer SystemeMagdeburgFR Germany
  2. 2.Institut für Systemdynamik und RegelungstechnikStuttgartFR Germany
  3. 3.Faculty of Engineering and Applied ScienceMemorial University of Newfoundland St. John’sNewfoundlandCanada

Personalised recommendations